Dans cet article on démontre qu’un feuilletage holomorphe de codimension un dans , n’a pas de minimaux non triviaux. On démontre aussi que pour , il n’existe pas de surfaces de Levi plates, analytiques réelles, dans .
In this paper we prove that holomorphic codimension one singular foliations on have no non trivial minimal sets. We prove also that for , there is no real analytic Levi flat hypersurface in .
@article{AIF_1999__49_4_1369_0, author = {Neto, Alcides Lins}, title = {A note on projective {Levi} flats and minimal sets of algebraic foliations}, journal = {Annales de l'Institut Fourier}, pages = {1369--1385}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {49}, number = {4}, year = {1999}, doi = {10.5802/aif.1721}, mrnumber = {2000h:32047}, zbl = {0963.32022}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1721/} }
TY - JOUR AU - Neto, Alcides Lins TI - A note on projective Levi flats and minimal sets of algebraic foliations JO - Annales de l'Institut Fourier PY - 1999 SP - 1369 EP - 1385 VL - 49 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1721/ DO - 10.5802/aif.1721 LA - en ID - AIF_1999__49_4_1369_0 ER -
%0 Journal Article %A Neto, Alcides Lins %T A note on projective Levi flats and minimal sets of algebraic foliations %J Annales de l'Institut Fourier %D 1999 %P 1369-1385 %V 49 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1721/ %R 10.5802/aif.1721 %G en %F AIF_1999__49_4_1369_0
Neto, Alcides Lins. A note on projective Levi flats and minimal sets of algebraic foliations. Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1369-1385. doi : 10.5802/aif.1721. http://www.numdam.org/articles/10.5802/aif.1721/
[AL-N] Algebraic solutions of polynomial differential equations and foliations in dimension two, Springer Lecture Notes, 1345 (1988), 192-232. | MR | Zbl
,[BB] On the zeroes of meromorphic vector fields, Essais en l'honneur de De Rham, (1970) 29-47. | MR | Zbl
, ,[CLS1] Minimal sets of foliations on complex projective spaces, Publ. Math. IHES, 68 (1988) 187-203. | EuDML | Numdam | MR | Zbl
, and ,[CLS2] Foliations with algebraic limit sets, Ann. of Math., 135 (1992) 429-446. | MR | Zbl
, and ,[E] Pseudo-convexité locale dans les variétés Kahlériennes, Ann. Inst. Fourier, 25-2 (1975), 295-314. | EuDML | Numdam | MR | Zbl
,[G] Lectures on Algebraic Topology, W. A. Benjamin inc., 1967. | MR | Zbl
,[H] Differential Topology, Springer Verlag, N.Y., 1976. | Zbl
,[Ha] Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa, serie 3, vol. 16 (1962), 367-397. | EuDML | Numdam | MR | Zbl
,[HL] Theory of Functions on Complex Manifolds, Birkhäuser, 1984. | Zbl
and ,[M] Morse Theory, Annals of Mathematics Studies 51, Princeton University Press, 1963. | Zbl
,[MB] Some remarks on indices of holomorphic vector fields, Prépublication 97, Université de Bourgogne (1996). | Zbl
,[S] Techniques of extension of analytic objects, Marcel Dekker Inc., New-York, 1974. | Zbl
,[Sm] On gradient dynamical systems, Ann. of Math., 74 (1961). | Zbl
,[ST] Gap-sheaves and extension of coherent analytic subsheaves, Lect. Notes in Math., 172 (1971). | MR | Zbl
and ,[T] Domaines pseudo-convexes sur les variétés Kahlériennes, Jour. Math. Kyoto University, 6-3 (1967), 323-357. | MR | Zbl
,[To] Tracce delle funzioni olomorfe sulle sottovarietà analitiche reali d'una varietà complessa, Ann. Scuola Norm. Sup. Pisa, (1966), 31-43. | Numdam | MR | Zbl
,Cité par Sources :